Recently developed mathematical models of subsidence in extensional basins provide a good basis for forward modeling. However, the large number of parameters to be specified by the user makes it difficult not only to do the modeling itself, but also to judge the meaning of the results. We present a new method for automatic searching of the best-fitting parameter set of 2D basin formation model. Weighted goal functions are used in the minimization process by the inverse problem solver algorithm. The nominal parameter set in the present case includes profiles of the crustal and subcrustal thinning factors, and the level of lithosphere necking. The method was tested on synthetic data with parameters that were perturbed beforehand. With some restrictions, the algorithms are capable of resolving such perturbations. The inversion technique has been applied to two profiles crossing the Dnieper-Donets Basin (Ukraine). The crustal thinning factors obtained argue for a scissors-like style of basin opening. High subcrustal thinning values are necessary in order to explain the abnormally thick Carboniferous section in the basin. These values should be treated as cumulative ones due to the currently unresolvable influence of other rifting-related processes, particularly phase transitions. ¿ 2001 American Geophysical Union